Multiphase and reactive fluid flow in porous media is often unstable, and highly heterogeneous: inherent microstructural heterogeneity leads to the emergence of preferential pathways, where most of the flow is focused in a small portion of the medium. Furthermore, strong hysteresis and rate-dependence are frequently observed. This complex behaviour is further corroborated by interactions between the fluids and the solid matrix, e.g. fracturing and dissolution. Understanding, predicting and controlling these phenomena is crucial in various applications across scales, from filtration, desalinization or microfluidics to soil infiltration, evapotranspiration, contamination and remediation, sediment transport, enhanced energy recovery or carbon geosequestration.

I will start with several examples of nonequilibrium flows from my research, where we combine numerical simulations, experiments, and theory to expose the underlying mechanisms. Wettability effects, in particular wetting-dewetting hysteresis, would be discussed in more depth. I will present a novel model, validated against laboratory experiments, that for the first time allows to establish a direct link between local, microscopic capillary instabilities (Haines jumps) and hysteresis in the macroscopic pressure-saturation relationship. Our approach provides a physically-grounded description of the nonequilibrium (metastable) nature of multiphase flow in porous and fractured media, and of the memory properties associated with it.